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Question
Evaluate without using trigonometric tables:
`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`
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Solution
`cos^2 26^@ + cos 64^@ sin 26^@ + tan 36^@/cot 54^@`
`= cos^2 26^@ + cos(90^@ - 26^@) sin 26^@ + tan 36^@/(cot(90^@ - 36^@))`
`= cos^2 26^@ + sin 26^@.sin26^@ + tan36^@/tan36^@` `[∵ cos(90^@ - theta) = sin theta, cot(90^@ - theta) = tan theta]`
`= cos^2 26^@ + sin^2 26^@ + 1`
`= 1 + 1 [∵ cos^2 theta + sin^2 theta = 1]`
= 2
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